MOSCOW, June 12 (Reuters) - A protest rally in Moscow onTuesday will test the ability of Russian opposition leaders tomaintain pressure on President Vladimir Putin in the face oftough new tactics that show he is determined to quash theirchallenge to his rule.

Opposition activists vowed to push ahead with plans for thefirst big rally since Putin's May 7 inauguration, a day afterpolice searched the homes of opposition leaders in raids Kremlincritics said smacked of the era of Soviet dictator Josef Stalin.

Federal investigators summoned prominent opposition leadersto appear for questioning just one hour before the scheduledstart of the demonstration.

The moves signalled a harsher approach to dissent at thestart of the former KGB officer Putin's new six-year term aspresident.

On Friday, he signed a law increasing fines, in some casesmore than 100-fold, for violations of public order atdemonstrations, despite warnings from his human rights councilthat it was an unconstitutional infringement on free assembly.

Police and investigators raided their Moscow apartments on asleepy morning in the middle of a three-day weekend, seizingcomputer drives and discs, photographs and other belongings asarmed guards stood outside.

"People barged in at 8 a.m., gave me no chance to getdressed, robbed the apartment, humiliated me," Sobchak said in aTwitter post. "I never thought we would return to suchrepression in this country."

"They rifled through everything, every wardrobe, in thetoilet, in the refrigerator. They searched under the beds,"Udaltsov, who was summoned for questioning along with his wifeon Tuesday, told reporters of the search of their home.

Police left Navalny's apartment 13 hours after they entered,carrying boxes. Navalny emerged later and told reporters thesummons was clearly aimed to keep him from the rally but vowedthat he would attend.

In power since 2000, Putin won a third presidential term inMarch despite a series of protests that drew tens of thousandsinto the streets, angry over alleged fraud in a Decemberparliamentary election won by his United Russia party.

Many protesters were middle-class city dwellers who havebenefitted from the oil-fuelled boom Russia has experiencedduring Putin's years at the helm but want more say in politicsand fear his prolonged rule will bring economic stagnation.

"SCARE TACTICS"

Police largely left those earlier protests alone but beganto crack down after Putin's election, beating protesters at therally on May 6 and repeatedly dispersing groups trying to set upOccupy-style permanent protests since then, briefly detaininghundreds.

They have detained 12 people over violence at the May 6protest on charges punishable by more than a year in jail, andthe latest summonses seemed to carry the implicit threat thatopposition leaders could potentially face similar charges.

Monday's searches sparked a wave of angry comment.

"Vova is crazy," one Twitter user wrote, referring to Putinby the common nickname for Vladimir. Others messaged under thetag that translates as "hello1937" - a reference to thedeadliest year of Stalin's repression.

"What we are witnessing today is in essence the year 1937,"opposition activist Yevgenia Chirikova said at an emergencymeeting in a cramped office to discuss plans for the protest.She said the searches and summonses were clearly a scare tactic.

Udaltsov predicted it would backfire.

"Some people may get scared, but people are less frightenednow" following the winter protests, he told reporters. "They aremore active, and I think even more people will come than hadinitially planned to.

"They are digging themselves a pit - deeper and deeper," hesaid of Putin and United Russia. The party lost dozens of seatsin the parliamentary vote, despite allegations of fraud in itsfavour, but still holds a majority.

Putin used that majority last week to rush the lawdrastically increasing fines through parliament, a move Kremlincritics said was aimed to suppress dissent.

Under the law, a participant at a gathering at which publicorder is deemed to have been violated with injury or damage toproperty can be fined as much as 300,000 roubles ($9,200), about60 times more than the previous maximum.

Opposition leaders have permission for Tuesday's march andrally in Moscow, but fines can be imposed for minor violationssuch as blocking traffic, and opposition leaders warnedprotesters to beware of actions likely to provoke a policeresponse.